A spectral limited-area primitive-equation model with a time-dependent lateral boundary condition is described.The model is nested in one way to a low resolution model.A spectral representation of the horizontal fields of prognostic variables is performed by introducing a modified double Fourier series.This series is composed of the usual orthogonal double Fourier series, that is suitable for prediction in the limited-area with a free-slip wall boundary condition, and a few additional bases by which the boundary condition which does not belong to the wall condition will be satisfied.Fluxes of mass, momentum, energy, etc.across the boundary can be specified using the additional bases.The proposed spectral method prescribes the amplitude of the additional bases, using the historical data from a coarse-mesh model forecast.The model predicts the amplitude of only the orthogonal bases that satisfy the wall boundary condition.A boundary relaxation technique is incorporated in order to reduce the amplitude of a spurious solution near the boundary due to ill-posed lateral boundary condition.A one-dimensional, linear advection equation is integrated by the present spectral method and by a grid-point method.The comparison of these two methods reveals that the spectral method give far better results than those of the grid point method.This is mainly due to the improved accuracy in estimating horizontal derivatives in the spectral method i.e., the computational dispersion and the systematic phase error that are unavoidable in the grid-point method are completely excluded in the spectral method.The spectral formulation of a limited-area model is applied to the Japan Meteorological Agency (JMA) operational grid-point 12-level fine-mesh limited-area model (12L-FLM; March, 1983 -) and the forecasts of the two 12L-FLMs are compared.The spectral 12L-FLM almost perfectly duplicates the forecast of the grid-point 12L-FLM for relatively large-scale disturbances, within the resolution limit of the latter.However, the forecast of the spectral 12L-FLM is superior to the grid-point model for relatively small-scale disturbances.The compared case includes a well-organized intense typhoon in the initial field.The horizontal scale of the typhoon is almost marginal to be resolved by the grid-point 12L-FLM.The predicted typhoon by the spectral model is more realistically intense and symmetric than that by the grid-point model.The amount of computation required by the spectral 12L-FLM, whose transform grid is the same as that of the grid-point model, is 20∼30 per cent larger than the amount required by the grid-point 12L-FLM.We conclude from this that the computational economy of the spectral 12L-FLM is practically superior to the grid-point 12L-FLM, since the effective resolution of the spectral model is about 1.5times better than the grid-point model.We plan to apply the spectral method to the next operational limited-area model in JMA.
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